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Notes towards a research report

Key ideas for a report

Frame established by keywords for the learning context:

  • visualisation/commentary; motivation/confidence; questions/exercises/problem solving
  • experience/interaction; frustration/perseverance; confusions/constructions/understanding

potential for CS student to learn mathematics

Arteesha - students don't look at the supplementary interactive materials

Sirandjivy - don't need to understand in order to do well in the exam

Stelios - pupil: why shouldn't I do this? - [teacher] because you'll lose marks in the exam

So would students look at construction?

capacity to learn 'what a vector is' is related to capacity to imagine what it can represent and what can represent it [Jamesian concept of 'substitution']

Thesis: "EM has potential to support new kinds of learning"

Do you agree with this?

If not, is this because (e.g.):

  • you don't consider EM to be essentially different from other approaches
  • EM technology is too immature
  • construction principles aren't accessible to the learner

Joe: If we can't build these models with our experience, how can a beginner do it?

If you agree / sympathise with the thesis, what do you think is required:

  • by way of EM-based learning environments?
  • by way of EM tool support?

"Rich picture" - seen many resources

distinction between goal-oriented procedural and exploratory state-as-experienced [cf. procedural, declarative, 'definitive']

SBR: 13 year olds going from one place to another on campus - you don't encourage them to savour the present moment

Project hasn't emphasised working towards goals: "How was it for you?" boring? ill-motivated?

Products of the study

Slogan: EM as ... AND ... not ...OR...

Three topics/potential outcomes of interest:

  1. new learning resources
  2. new tools / environments / technology
  3. paper-report

1. New learning resources

Central idea: webpage of unprecedented nature cf. projected EM webpage c. 2004

Not just a webpage incorporating - and with rich collection of links to - different kinds of resource, but allowing these to be integrated and subject to experimental interaction and personalisation

cf. personalising through annotation by humanities computing scholars / adaptation

not primarily adaptation but quality of the interaction - 'making conjunctions'

not only what hypermedia suggests - the semantic web - network of disjoint resources - at least as far as the underpinning computing infrastructure is concerned

But concerned with EM and learning as potentially integrating these resources - cf. knowing the connection between constructing eigenvectors and representing a linear map

semantic web??
- more like the semantic world/ocean/country/terrain - web as a medium and as a network

To appreciate terrain have to be able to travel - but not enough to be able to travel

Travelling that promotes appreciation of the terrain have to be able to travel - cf. walking / driving / flying

Integration of resources? cf. wild animals:
in the picture book / on TV / in zoo / in safari park / in the wild
nuances: driving and/or walking in safari park

Enriching existing resources, such as:

  • (commentary - illustration/animated [exercise])*
  • 'serious' games (e.g. matrix Countdown, three vector addition for step-climbing
  • situated simulation (e.g. death-trap case study

Relationship to GeoGebra

Relationship to existing approaches in the Intelligent Tutoring Systems arena:

  • inquiry-based learning [RASHI]
  • constraint-based modelling

procedural vs conceptual learning, blended learning

Appreciating limitations - cf. Dijkstra's "testing can never establish program correctness" cf. giving model answers to exam questions / issue raised by the concept of "correct answer"

What kind of construction promotes understanding? cf. 'ingeniously guided discovery'

  • notion of a path to ensure progress [cf. SBR's vision for the lecture notes)
  • challenges of determining whether a construction is "a good learning experience"

Consider the two versions of the linear independence construction proposed by SBR / benefits of factoring out the effect of the accidental "y<0 means up the canvas"

To what extent do we want EM construction to be "more routine" - cf. JB re-building from scratch

Discussion of the ODA framework relevant to this

Identifying other exercises that could be instructive e.g. amplifying what can be done with the eigenvector scenario, as well as what needs to be done to make this scenario informative e.g. square of M has same eigenvalues as M / change of basis as in JB / visualisation of linear maps - solution to CS131 Question 7(b)

Construals to address multiple viewpoints, e.g.:

  • vector as displacement / as movement / as column; with or without coordinates
  • equation of a line in vector and symbolic form. as visualised

Exercises to address fluency - doing things against time, presenting in a timely way

New tools / environments / technology

Tightly-coupled cycle that is experienced as in one and the same state

(HUMAN inputs / constructs / reflects | COMPUTER records/ represents / generates experience)*

Integrating other resources with EM resources?

... with each other / Sylvester vectors / BBC + Khan Academy + MyMath / latex2html

Anonymous comment in conversation overheard: "you learn how to lie with s/w" - where not to go when giving a demo - cf. relevance of the terrain metaphor in EM development

Possible vision for JS-EDEN

Generating generic definition a is f(b,c,d) where the context supplies the interpretation of f, a, b, c and d.

Two contexts that are typically active: interpreting a definition as associating an internal and an external representation with an observable. E.g. observable v might have v.w / v subscript 1 notation at interface to construct internal v.dot(w) / v.e(1) internally, and vLine with it externally. In general, want such interpreters for every agent - e.g. mouse could have means to move point.

Different modes of parsing associated with different input windows

Adapting JS-EDEN for more effective modelling ...

  • Reflect on after() in managing experience - contrast with "proceed-on-click"
  • Variety of interface agency - beyond sliders (cf. Blender), more nuanced mouse actions
  • Issues concerning script management
  • Collaboration
  • Persistence

allowing many kinds of agency - e.g. draggable for positioning labels, brackets etc

webpage for observables and DMT

cameras for snapshots and videos as a conceptual adjunct ("marrying procedural with declarative") cf. "mathlets" reference
backdrops as in grids, external images and snapshots

Improved documentation and support for the developer

Evaluating qualities and limitations of EM tools such as JS-EDEN: appreciating qualities of OO/GeoGebra
understanding the role of the expedient - "a underlined" / blackboards-whiteboards-computers
importance of conventions form context as in "a underbar for vector and a for magnitude"

Conclusions etc

Limitations of our study - and how these might be addressed. Especially lack of empirical study of the learning subjects.